Recent content by jodecy

ok so i worked it out using the subst of u = 1 - x^2 and got the answer to be -1/3 (1-x^2) ^ 3/2 + c. however the original method i used was that presented to me by my lecturer so I'm wondering ...

i believe it was given in a lecture i had so i assumed is that a wrong assumption?

Homework Statement required to prove that ∫()[, ] =∫(−) [+, +] where f is a real valued function integrable over the interval [a, b] Homework Equations ∫() [, ]=()−() The Attempt at a Solution ∫() [b, a]=()−() ∫(−) [+, +]=(+−)−(+−)=()−() ∴∫()[, ] =∫(−) [+, +]...

ohhhh so i need to state θ = arcsinx therefore my answer in terms of x would be -1/3 cos^3(arcsinx )? when i come back i'll try subst with u = 1-x^2

Homework Statement find the indefinite integral of ∫x√(1-x^2) dx Homework Equations The Attempt at a Solution ∫x√(1-x^2) dx let x = sinθ dx = cosθ dθ now sin^2θ + cos^2θ = 1 => cosθ = √1-sin^2θ ( for the form √(1-x^2)) ∫x√(1-x^2) dx => ∫sinθ (√1-sin^2θ) cosθ dθ =>...